Find the intervals in which the function f given by f (x) = 2x² - 3x is
(a) Increasing   (b) Decreasing

Solution:

Increasing functions are those functions that increase monotonically within a particular domain,

and decreasing functions are those which decrease monotonically within a particular domain.

The given function is

f (x) = 2x² - 3x

Hence,

On differentiating wrt x,we get

f' (x) = 4x - 3

Therefore,

f' (x) = 0

If the derivative is greater than 0 then the function is an increasing function.

Þ x = 3/4

In (- ∞, 3/4),

f' (x) = 4x - 3 < 0

Hence, f is strictly decreasing in (- ∞, 3/4).

In (3/4, ∞),

f' (x) = 4x - 3 > 0

Hence, f is strictly increasing in (3/4, ∞)

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.2 Question 4

Find the intervals in which the function f given by f (x) = 2x² - 3x is (a) Strictly increasing (b) Strictly decreasing

Summary:

The intervals in which the function f given by f (x) = 2x² - 3x is strictly decreasing in (- ∞, 3/4) and strictly increasing in (3/4, ∞)